We study a superconducting artificial atom which is represented by a single
Josephson junction or a Josephson junction chain, capacitively coupled to a
coherently driven transmission line, and which contains exactly one residual
quasiparticle (or up to one quasiparticle per island in a chain). We study the
dissipation in the atom induced by the quasiparticle tunneling, taking into
account the quasiparticle heating by the drive. We calculate the transmission
coefficient in the transmission line for drive frequencies near resonance and
show that, when the artificial atom spectrum is nearly harmonic, the intrinsic
quality factor of the resonance increases with the drive power. This
counterintuitive behavior is due to the energy dependence of the quasiparticle
density of states